Semiclassical determination of adiabatic barriers on a three-dimensional potential energy surface

Abstract

A recently proposed method, based on periodic orbits, for finding vibrationally adiabatic barriers and wells in collinear collisions is generalized to the full three-dimensional case. The main idea is a consistent use of the adiabatic approximation—one first solves for the fast vibrational motion to obtain an effective Hamiltonian for the slower bend motion which in turn is solved to obtain an effective Hamiltonian for the overall rotation. The method is applied to the hydrogen exchange reaction. We find the bend-vibration adiabatic barrier levels for the H2(v=1) state. The zero point motion in the bend degree of freedom is found to be substantial (0.1 eV) and is a source for nonnegligible discrepancies between approximate theories such as the infinite order sudden and quasiclassical trajectory approach and exact quantal scattering computations. Having found the barrier levels we are able to evaluate the collision cross section. Our analysis points out that differences between experimental cross sections and theoretical predictions may be due to inaccuracy in the potential energy surfaces. The available surfaces probably overestimate the adiabatic barrier height.